重心与多边形最远点之间的距离

我有一个乡村多边形图层，其中有600万条记录。我已经计算出每个村庄的质心。我想找到质心和每个多边形的最远节点之间的距离。检查下面的图像以供参考。黑线是多边形边界。

看来您正在使用MapInfo。“距离计算器”（在工具管理器中找到）有很多选项，我认为它也可以处理此任务。这里有一篇关于它的文章：http : //web.pb.com/mapinfopro-jul-2013/Toolbox-Distance-Calculator

使用PostGIS，我使用ST_ConvexHull简化了多边形以获得更快的结果：

获得最远的积分：

SELECT Villages_v4_Trial_region.geom as FarPoint from (
SELECT ST_PointN(ST_ExteriorRing(ST_ConvexHull(Villages_v4_Trial_region.geom)),
generate_series(1, ST_NPoints(ST_ExteriorRing(ST_ConvexHull(Villages_v4_Trial_region.geom))))) as points, 
geom
FROM Villages_v4_Trial_region
ORDER BY ST_MaxDistance(points,ST_Centroid(Villages_v4_Trial_region.geom)) DESC
LIMIT 1;

如果您有兴趣从质心创建一个圆，请执行以下操作：

SELECT ST_Buffer(Center,ST_Distance(Center,FarPoint)) as Circle
FROM (
SELECT Villages_v4_Trial_region.geom as FarPoint, Center from (
    SELECT ST_PointN(ST_ExteriorRing(ST_ConvexHull(Villages_v4_Trial_region.geom)),
    generate_series(1, ST_NPoints(ST_ExteriorRing(ST_ConvexHull(Villages_v4_Trial_region.geom))))) as points,
    ST_Centroid(Villages_v4_Trial_region.geom) as Center, 
    geom
    FROM Villages_v4_Trial_region
    ) as Villages_v4_Trial_region
    ORDER BY ST_MaxDistance(points,Center) DESC
    LIMIT 1) as foo;

使用下一个PyQGIS代码：

from math import sqrt

layer = iface.activeLayer()

feats = [ feat for feat in layer.getFeatures() ]

n = len(feats)

centroids = [ feat.geometry().centroid().asPoint() for feat in feats ]
polygons = [ feat.geometry().asPolygon()[0] for feat in feats ]

lengths = []

for i, pol in enumerate(polygons):
    max_dist = 0
    idx_j = 0
    for j, point in enumerate(pol):
        dist = sqrt(centroids[i].sqrDist(point))
        if dist > max_dist:
            max_dist = dist
            idx_j = j
    print i, idx_j, max_dist
    lengths.append([centroids[i], pol[idx_j]])

crs = layer.crs()
epsg = crs.postgisSrid()

uri = "LineString?crs=epsg:" + str(epsg) + "&field=id:integer""&index=yes"

mem_layer = QgsVectorLayer(uri,
                           'max_distance',
                           'memory')

prov = mem_layer.dataProvider()

feats = [ QgsFeature() for i in range(n) ]

for i, feat in enumerate(feats):
    feat.setAttributes([i])
    feat.setGeometry(QgsGeometry.fromPolyline(lengths[i]))

prov.addFeatures(feats)

QgsMapLayerRegistry.instance().addMapLayer(mem_layer)

和这个shapefile（具有11个功能）：

我得到了一个存储层，折线是质心和每个多边形（特征）的最远点之间的距离；在下一张图片中可以看到：

在QGIS的Python控制台上，它还打印了要素索引，要素中距质心的距离为最大，最后是最大距离的点的索引。

看起来您正在使用MapInfo，这是我不久前为正在使用的内部工具编写的MapBasic函数。它以源节点（质心点）和区域对象（多边形）为参数，并从源点返回多边形中最远节点处的点对象。

Function GetFurthest(ByVal oNode1 as Object, ByVal oObj as Object) as Object

Dim sourceE,sourceN,East,North,Longest,Dist as Float,
    nNodes,nPolys,i,j as SmallInt,
    oNode2 as Object

    sourceE = CentroidX(oNode1)
    sourceN = CentroidY(oNode1)
    Longest = 0

    nPolys = ObjectInfo(oObj,OBJ_INFO_NPOLYGONS)
    For i = 1 to nPolys
        nNodes = ObjectInfo(oObj,OBJ_INFO_NPOLYGONS+nPolys)
        For j = 1 to nNodes
            East = ObjectNodeX(oObj,i,j)
            North = ObjectNodeY(oObj,i,j)
            Dist = Distance(sourceE,sourceN,East,North,"m")
            If Dist > Longest then
                Longest = Dist
                oNode2 = CreatePoint(East,North)
            End if
        Next
    Next

    GetFurthest = oNode2

End Function